Exhibit 99.1

STOCKHOLDER TENDER AGREEMENT

STOCKHOLDER TENDER AGREEMENT (this “Agreement”), dated as of May 7, 2012, is made and entered into by and among UNICOM Systems, Inc., a California corporation (“Parent”), UNICOM SUB ONE, INC., a Delaware corporation and a wholly owned subsidiary of Parent (“Merger Sub”) and the stockholders of GTSI Corp., a Delaware corporation (the “Company”) listed on the signature pages hereto (each a “Stockholder”).

WHEREAS, each Stockholder is, as of the date hereof, the record and/or beneficial owner (as defined in Rule 13d-3 under the Securities Exchange Act of 1934, as amended (the “Exchange Act”) of the number of shares of Common Stock, par value $0.005 (the “Company Common Stock”) set forth opposite the name of such Stockholder on Schedule I hereto; and

WHEREAS, concurrently with the execution and delivery of this Agreement, the Company is entering into an Agreement and Plan of Merger (the “Merger Agreement”) with Parent and Merger Sub, that provides, among other things, for Merger Sub to commence a cash tender offer for all of the issued and outstanding shares of Company Common Stock (the “Offer”) and the merger of Merger Sub with and into the Company (the “Merger”) upon the terms and subject to the conditions set forth in the Merger Agreement (capitalized terms used herein without definition shall have the respective meanings specified in the Merger Agreement).

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements set forth herein and in the Merger Agreement, and intending to be legally bound hereby, the parties hereto agree as follows:

SECTION 1. Representations and Warranties of Stockholder. Each Stockholder hereby represents and warrants as follows:

(a) Such Stockholder (i) is the record and/or beneficial owner of the shares of Company Common Stock (together with any shares of Company Common Stock that such Stockholder may acquire at any time in the future during the term of this Agreement, the “Shares”) set forth opposite such Stockholder’s name on Schedule I to this Agreement and (ii) neither holds nor has any beneficial ownership interest in any other shares of Company Common Stock except for the Shares set forth on Schedule I to this Agreement or any restricted stock, options, stock appreciation rights (including any granted pursuant to a Company Stock Plan), or warrants to acquire shares of Company Common Stock or other right or security convertible into or exercisable or exchangeable for shares of Company Common Stock.

(b) Such Stockholder has the legal capacity to execute and deliver this Agreement and to consummate the transactions contemplated hereby.

(c) This Agreement has been validly executed and delivered by such Stockholder and, assuming this Agreement constitutes a valid and binding obligation of the other parties hereto, constitutes the valid and binding obligation of such Stockholder, enforceable against such Stockholder in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and other laws of general application affecting enforcement of creditors’ rights generally, and (ii) that the

availability of the remedy of specific performance or injunctive or other forms of equitable relief may be subject to equitable defenses and would be subject to the discretion of the court before which any proceeding therefor may be brought.

(d) Neither the execution and delivery of this Agreement nor the consummation by such Stockholder of the transactions contemplated hereby will result in a violation of, or a default under, or conflict with, any contract, trust, commitment, agreement, understanding, arrangement or restriction of any kind to which Stockholder is a party or by which Stockholder or Stockholder’s assets are bound. The consummation by such Stockholder of the transactions contemplated by this Agreement will not (i) violate any provision of any judgment, order or decree applicable to such Stockholder or (ii) require any consent, approval or notice under any statute, law, rule or regulation applicable to Stockholder other than (x) as required under the Exchange Act and the rules and regulations promulgated thereunder and (y) where the failure to obtain such consents or approvals or to make such notifications, would not, individually or in the aggregate, prevent or materially delay the performance by Stockholder of any of its obligations under this Agreement.

(e) The Shares and the certificates, if any, representing the Shares owned by such Stockholder are now, and at all times during the term hereof will be, held by such Stockholder, by a nominee or custodian for the benefit of such Stockholder or by the paying agent (if any) for the Offer, free and clear of all liens, claims, security interests, proxies, voting trusts or agreements, options, rights (other than community property interests), understandings or arrangements or any other encumbrance or restriction whatsoever on title, transfer, or exercise of any rights of a Stockholder in respect of such Shares (collectively, “Encumbrances”), except for (i) any such Encumbrances arising hereunder (in connection therewith any restrictions on transfer or any other Encumbrances have been waived by appropriate consent), and (ii) Encumbrances imposed by federal or state securities laws (collectively, “Permitted Encumbrances”).

(f) No broker, investment bank, financial advisor or other person is entitled to any broker’s, finder’s, financial adviser’s or similar fee or commission in connection with the transactions contemplated hereby based upon arrangements made by or on behalf of such Stockholder (except for fees payable by the Company to Raymond James & Associates, Inc. and Stout Risius Ross, Inc. as advisors to the Company in connection with the transactions contemplated by the Merger Agreement).

SECTION 2. Representations and Warranties of the Buyer Parties. Parent and Merger Sub hereby represent and warrant as follows:

(a) Each of Parent and Merger Sub is a corporation duly organized, validly existing and in good standing under the laws of the State of California and Delaware, respectively, and each of Parent and Merger Sub has all requisite corporate power and authority to execute and deliver this Agreement and the Merger Agreement and to consummate the transactions contemplated hereby and thereby, and has taken all necessary corporate action to authorize the execution, delivery and performance of this Agreement and the Merger Agreement.

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(b) This Agreement and the Merger Agreement have been duly authorized, executed and delivered by Parent and Merger Sub, and constitute the valid and binding obligations of Parent and Merger Sub, enforceable against each of them in accordance with their terms, except (i) as limited by applicable bankruptcy, insolvency, reorganization, fraudulent conveyance, moratorium and other laws of general application affecting enforcement of creditors’ rights generally and (ii) the availability of the remedy of specific performance or injunctive or other forms of equitable relief may be subject to equitable defenses and would be subject to the discretion of the court before which any proceeding therefor may be brought.

(c) Neither the execution and delivery of this Agreement or the Merger Agreement by Parent and Merger Sub nor the consummation by Parent and Merger Sub of the transactions contemplated hereby or thereby will result in a violation of, or a default under, any contract, trust, commitment, agreement, understanding, arrangement or restriction of any kind to which Parent or Merger Sub are parties or by which Parent or Merger Sub or their respective assets are bound. The consummation by Parent and Merger Sub of the transactions contemplated by this Agreement will not (i) violate any provision of any judgment, order or decree applicable to Parent or Merger Sub or (ii) require any consent, approval, order, authorization or permit of, or declaration, registration, filing with, or notification to, any Governmental Authority, except for (w) applicable requirements, if any, of (A) the Exchange Act, including, without limitation, the filing with the SEC of the Schedule TO, (B) the DGCL and (C) NASDAQ, (x) those required by the HSR Act, (y) the filing of customary applications and notices, as applicable with any regulatory authority, and (z) where the failure to obtain such consents or approvals or to make such notifications, would not, individually or in the aggregate, prevent or materially delay the performance by Parent or Merger Sub of their obligations under this Agreement and the Merger Agreement.

SECTION 3. Tender of the Shares.

(a) Unless (i) the Offer is terminated or withdrawn by Merger Sub, (ii) there is any decrease in the price per share of Common Stock payable in the Offer or any change in the form of consideration payable in the Offer, (iii) a Change of Recommendation is made under the Merger Agreement,(iv) the Merger Agreement is terminated in accordance with its terms or (v) this Agreement shall have been terminated under Section 8 hereof, each Stockholder hereby agrees that it shall irrevocably, subject to the terms of this Agreement, tender (and deliver any certificates evidencing) its Shares, or cause its Shares to be irrevocably, subject to the terms of this Agreement, tendered, into the Offer promptly following, and in any event no later than the tenth (10th) business day following the commencement of the Offer pursuant to Section 1.1 of the Merger Agreement in accordance with the procedures set forth in the Offer Documents, free and clear of all Encumbrances (other than Permitted Encumbrances); provided, however, that each Stockholder may withdraw its Shares from the Offer at any time following the termination of this Agreement or as otherwise provided pursuant to this Section 3 or Section 8 hereof.

(b) Each Stockholder agrees that once the Shares are tendered into the Offer, Stockholder will not withdraw any Shares from the Offer unless and until (i) the Offer shall have been terminated in accordance with the terms of the Merger Agreement, (ii) there is any decrease in the price per share of Common Stock payable in the Offer or any change in the form of consideration payable in the Offer, (iii) a Change of Recommendation is made under the Merger Agreement, (iv) the Merger Agreement is terminated in accordance with its terms or (v) this Agreement shall have been terminated in accordance with Section 8 hereof.

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(c) Each Stockholder hereby waives, on its own behalf on behalf of any recordholder of any of the Shares, any rights of appraisal or rights to dissent from the Merger that Stockholder or any such recordholder may have under Section 262 of the DGCL, and hereby agrees not to assert any such rights of appraisal or dissent.

SECTION 4. Transfer of the Shares; Other Actions.

(a) Prior to the termination of this Agreement, except as otherwise provided herein or in the Merger Agreement, each Stockholder shall not: (i) transfer, assign, sell, gift-over, hedge, pledge or otherwise dispose (whether by sale, liquidation, dissolution, dividend or distribution) of, enter into any derivative arrangement with respect to, create or suffer to exist any Encumbrances (other than Permitted Encumbrances) on or consent to any of the foregoing (“Transfer”), any or all of the Shares or any right or interest therein; (ii) enter into any contract, option or other agreement, arrangement or understanding with respect to any Transfer; (iii) grant any proxy, power-of-attorney or other authorization or consent with respect to any of the Shares with respect to any matter that is, or that is reasonably likely to be exercised in a manner, inconsistent with the transactions contemplated by the Merger Agreement or the provisions thereof; (iv) deposit any of the Shares into a voting trust, or enter into a voting agreement or arrangement with respect to any of the Shares; or (v) knowingly, directly or indirectly, take or cause the taking of any other action that would restrict, limit or interfere with the performance of such Stockholder’s obligations hereunder or the transactions contemplated hereby, excluding any bankruptcy filing.

(b) Each Stockholder agrees that it shall not become a member of a “group” (as that term is used in Section 13(d) of the Exchange Act) with respect to any shares of Company Common Stock, Company Stock Options, Company Stock-Based Securities or any other voting securities of the Company for the purpose of opposing or competing with or taking any actions inconsistent with the transactions contemplated by the Merger Agreement; provided, however, this Section 4(b) shall not apply if (i) the Offer is terminated or withdrawn by Merger Sub, (ii) there is any decrease in the price per share of Common Stock payable in the Offer or any change in the form of consideration payable in the Offer, (iii) a Change of Recommendation is made under the Merger Agreement, (iv) the Merger Agreement is terminated in accordance with its terms or (v) this Agreement shall have been terminated under Section 8 hereof.

(c) Notwithstanding the foregoing, each Stockholder may make (i) Transfers of Shares by will or by operation of law or other transfers for estate planning purposes or for charitable purposes, including gifts and donations, (ii) Transfers of Shares to an Affiliate, in each of (i) and (ii), such transferee shall agree in writing to be bound by this Agreement prior to the consummation of any such Transfer, and (iii) as Parent may otherwise agree in writing in its sole discretion.

(d) Upon receipt of payment in full for all of its Shares pursuant to the Merger Agreement, each Stockholder agrees that any and all rights incident to its ownership of Shares

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(including any rights to recover amounts, if any, that may be determined to be due to any stockholder or former stockholders of the Company), including but not limited to rights arising out of such Stockholder’s ownership of Shares prior to the transfer of such Shares to Merger Sub or Parent pursuant to the Offer or the Merger Agreement, shall be transferred to Merger Sub and Parent upon the transfer to Merger Sub or Parent of such Stockholder’s Shares.

SECTION 5. Voting Agreement. If (i) a meeting of the stockholders is necessary to consummate the Merger, and (ii) at the time proxies are solicited for such meeting, the Stockholder beneficially owns any shares of Company Common Stock, and if requested by Parent, Stockholder will execute a voting agreement with Parent, containing customary terms which are consistent with the terms and intent of this Agreement (including with respect to the limitations on Stockholder’s obligations hereunder), to vote the maximum number of shares of Company Common Stock beneficially owned by the Stockholder in support of the Merger.

SECTION 6. Directors and Officers. Notwithstanding anything herein to the contrary, this Agreement shall apply to each Stockholder solely in such Stockholder’s capacity as a holder of Company Common Stock, and not to any Stockholder or any representative of a Stockholder serving as a director of the Company in such capacity or in any other capacity.

SECTION 7. Further Assurances. Each party shall execute and deliver any additional documents and take such further actions as may be reasonably necessary or desirable to carry out all of the provisions hereof, including all of the parties’ obligations under this Agreement.

SECTION 8. Termination.

(a) This Agreement, and all rights and obligations of the parties hereunder, shall terminate immediately upon the earliest to occur of the following:

(i) termination of the Merger Agreement in accordance with its terms;

(ii) the Effective Time;

(iii) a Change in Recommendation under the Merger Agreement; or

(iv) the mutual written consent of Parent and the Stockholder.

(b) The Stockholders shall have the right to terminate this Agreement following (i) any decrease in the price per share of Common Stock payable in the Offer; or (ii) any change in the form of consideration payable in the Offer.

(c) Upon termination of this Agreement, except in the case of liability for any willful breach by any party to this Agreement prior to termination from which liability termination shall not relieve any such party, (i) all obligations of the parties under this Agreement will terminate, without any liability or other obligation on the part of any party hereto to any Person in respect hereof or the transactions contemplated hereby, and no party shall have any claim against another (and no person shall have any rights against such party), whether under contract, tort or otherwise, and (ii) each Stockholder shall be permitted to withdraw, and shall be deemed to have validly and timely withdrawn, their Shares pursuant to the Offer, provided however, that the termination of this Agreement shall not relieve any party from liability from any willful breach prior to such termination.

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(d) Sections 9 and 12(e) hereof shall survive the termination of this Agreement.

SECTION 9. Expenses. All fees and expenses incurred in connection with this Agreement and the transactions contemplated hereby shall be paid by the party incurring such fees or expenses, whether or not the Offer or the Merger is consummated.

SECTION 10. Public Announcements. Each Stockholder (in its capacity as a stockholder of the Company and/or signatory to this Agreement) shall not, nor shall it permit any of its Representatives to, make any public announcement regarding this Agreement and the transactions contemplated hereby, except as required for a Stockholder to comply with its obligations under the Exchange Act (including, but not limited to, the filing of an amendment to the Form 4 and/or Schedule 13D or 13G previously filed with the SEC by the Stockholders), the Bank Holding Company Act or rules of the NASDAQ or (z) as required by the SEC or any Governmental Authority. Each Stockholder (i) consents to and authorizes the publication and disclosure by the Company, Parent or Merger Sub and their its Affiliates of its identity and holding of the Shares and the nature of its commitments and obligations under this Agreement in any announcement or disclosure required by the SEC or other Governmental Authority in connection with the Offer, or in any other disclosure document in connection with the Offer, the Merger or in any of the other transactions contemplated by the Merger Agreement or this Agreement, and (ii) agrees promptly to give to the Company, Parent or Merger Sub any information it may reasonably require for the preparation of any such disclosure documents; provided, that the Stockholders shall have a reasonable opportunity to review and comment on any such announcement or disclosure prior to its publication, filing or disclosure. Stockholder agrees to promptly notify the Company, Parent and Merger Sub of any required corrections with respect to any written information supplied by it specifically for use in any such disclosure document, if and to the extent that any shall have become false or misleading in any material respect.

SECTION 11. Adjustments. In the event of (a) any stock dividend, stock split, merger, recapitalization, reclassification, combination, exchange of shares or the like of the capital stock of the Company on, of or affecting the Shares or (b) that any Stockholder shall become the beneficial owner of any additional shares of Company Common Stock, then the terms of this Agreement shall apply to the shares of Company Common Stock held by such Stockholder immediately following the effectiveness of the events described in clause (a) or such Stockholder becoming the beneficial owner thereof as described in clause (b), as though, in either case, they were Shares hereunder. In the event that Stockholder shall become the beneficial owner of any other securities entitling the holder thereof to vote or give consent with respect to the matters set forth in Section 5 hereof, then the terms of Section 5 hereof shall apply to such other securities as though they were Shares hereunder.

SECTION 12. Miscellaneous.

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(a) Other Activities. Notwithstanding anything to the contrary in this Agreement, nothing herein shall in any way limit a Stockholder or any affiliate of a Stockholder from engaging in any brokerage, investment advisory, financial advisory, anti-raid advisory, principal investing, merger advisory, financing, asset management, trading, market making, arbitrage, investment activity and other similar activities conducted in the ordinary course of their business.

(b) Notices. All notices, requests, claims, demands and other communications under this Agreement shall be in writing and shall be deemed given if delivered personally, sent via electronic mail (receipt confirmed), facsimile (receipt confirmed) or sent by a nationally recognized overnight courier (providing proof of delivery) to the parties at the following addresses (or at such other address for a party as shall be specified by like notice):

If to Stockholders, to:

The address set forth beside each Stockholder’s name listed on Schedule I.

If to Parent or Merger Sub to:

UNICOM Systems, Inc.

15535 San Fernando Mission Bl., Ste. 310

Mission Hills, CA 91345

Attention: Corry Hong, President and CEO

Fax: (818) 838-0776

with a copy to:

UNICOM Systems, Inc.

15535 San Fernando Mission Bl., Ste 310

Mission Hills, CA 91345

Attention: Gerard R. Kilroy, Esq.

Fax: (818) 838-0606

If to Company, to:

GTSI, Inc.

2553 Dulles View Drive, Suite 100

Herndon, VA 20171-5219

Attention: Sterling E. Phillips Jr., CEO

Fax: (703) 463-5101

with a copy to:

Holland & Knight LLP

1600 Tysons Boulevard, Suite 700

McLean, Virginia 22102

Attention: William J. Mutryn

Fax: (703) 720-8610

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(c) Headings. The headings contained in this Agreement are for reference purposes only and shall not affect in any way the meaning or interpretation of this Agreement.

(d) Counterparts. This Agreement may be executed in two or more counterparts, all of which shall be considered one and the same agreement and shall become effective when one or more counterparts have been signed by each of the parties and delivered to the other parties.

(e) Entire Agreement, Third-Party Beneficiaries. This Agreement (a) constitutes the entire agreement, and supersedes all prior agreements and understandings, both written and oral, among the parties with respect to the subject matter of this Agreement and (b) is not intended to confer, nor shall it confer, upon any Person other than the parties hereto any rights or remedies or benefits of any nature whatsoever.

(f) Governing Law, Jurisdiction. This Agreement shall be governed in all respects, including validity, interpretations and effect, by the laws of the State of Delaware applicable to contracts executed and to be performed wholly within such state without giving effect to the choice of law principles of such state.

(g) Waiver of Jury Trial. PARENT, MERGER SUB AND EACH STOCKHOLDER HEREBY IRREVOCABLY WAIVE ALL RIGHT TO TRIAL BY JURY IN ANY ACTION, PROCEEDING OR COUNTERCLAIM (WHETHER BASED ON CONTRACT, TORT OR OTHERWISE) ARISING OUT OF OR RELATING TO THIS AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THE ACTIONS OF STOCKHOLDER IN THE NEGOTIATION, ADMINISTRATION, PERFORMANCE AND ENFORCEMENT OF THIS AGREEMENT. EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT (A) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE EITHER OF SUCH WAIVERS, (B) IT UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF SUCH WAIVERS, (C) IT MAKES SUCH WAIVERS VOLUNTARILY, AND (D) IT HAS BEEN INDUCED TO ENTER INTO THIS AGREEMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 12(g).

(h) Assignment. Except in connection with permitted Transfers pursuant to Section 4(c) hereof, prior to the earlier to occur of (i) the termination of the Merger Agreement in accordance with its terms or (ii) the consummation of the Merger, neither this Agreement nor any of the rights, interests or obligations under this Agreement shall be assigned, in whole or in part, by operation of law or otherwise by any of the parties hereto without the prior written consent of the other parties. Any assignment in violation of the preceding sentence shall be void. Subject to the preceding two sentences, this Agreement will be binding upon, inure to the benefit of, and be enforceable by, the parties and their respective successors and assigns.

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(i) Severability of Provisions. If any term or other provision of this Agreement is invalid, illegal or incapable of being enforced by any rule of law or public policy, all other conditions and provisions of this Agreement shall nevertheless remain in full force and effect, insofar as the foregoing can be accomplished without materially affecting the economic benefits anticipated by the parties to this Agreement. Upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, the parties hereto shall negotiate in good faith to modify this Agreement so as to effect the original intent of the parties as closely as possible to the fullest extent permitted by applicable Law in an acceptable manner to the end that the transactions contemplated hereby are fulfilled to the extent possible.

(j) Specific Performance. The parties agree that irreparable damage would occur and that the parties would not have any adequate remedy at law in the event that any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached. It is accordingly agreed that the parties shall be entitled to an injunction or injunctions to prevent breaches of this Agreement and to enforce specifically the terms and provisions of this Agreement in any federal court located in the State of Delaware or in Delaware state court, this being in addition to any other remedy to which they are entitled at law or in equity.

(k) Amendment. No amendment or modification of this Agreement shall be effective unless it shall be in writing and signed by each of the parties hereto, and no waiver or consent hereunder shall be effective against any party unless it shall be in writing and signed by such party.

(l) Binding Nature. This Agreement is binding upon and is solely for the benefit of the parties hereto and their respective successors, legal representatives and assigns.

(m) No Recourse. Parent and Merger Sub agree that no Stockholder (in its capacity as a stockholder of the Company) will be liable for claims, losses, damages, liabilities or other obligations resulting from or related to the Merger Agreement or the Offer, including with respect to the Company’s breach of the Merger Agreement.

(n) No Ownership Interest. Except as otherwise provided herein, nothing contained in this Agreement shall be deemed to vest in Parent or Merger Sub any direct or indirect ownership or incidence of ownership of or with respect to the Shares. All rights, ownership and economic benefits of and relating to the Shares shall remain vested in and belong to Stockholder.

[signatures on following pages]

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IN WITNESS WHEREOF, each of the parties hereto has caused this Agreement to be duly executed and delivered as of the date first written above.

{Signature Page to Charitable Trust Stockholder Tender Agreement}

{Signature Page to Charitable Trust Stockholder Tender Agreement}

SCHEDULE I

{Signature Page to Johnson Stockholder Tender Agreement}

SCHEDULE I

{Signature Page to Lacy Stockholder Tender Agreement}

SCHEDULE I